Printable · GCSE Higher · ages 14-16

Geometry and measures worksheet — GCSE Higher

Fifteen questions across the geometry and measures statements at Higher tier. Choose the non-calculator filter to rehearse Paper 1, which counts for a third of the marks.

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Geometry and measures worksheet — GCSE Higher

Maths · GCSE Higher · Geometry and measures · Non-calculator · 15 questions

MathsUKwww.geekhero.co.uk

1.A circle with centre O has radius 17 cm. A chord AB is drawn so that the perpendicular distance from O to AB is 8 cm. Work out the length of the chord AB.
(a)15 cm
(b)30 cm
(c)25 cm
(d)9 cm
2.Shape S is enlarged by scale factor −1, centre (0, 0). Which single transformation has the same overall effect as this enlargement, for every point?
(a)A reflection in the y-axis
(b)A reflection in the x-axis
(c)A rotation of 180° about the origin
(d)No transformation — the shape is unchanged
3.A textbook contains the instruction 'Draw AB' and, on the next line, the statement 'AB = 5 cm'. Which statement about the notation AB is correct?
(a)The length must be written as |AB|, not AB
(b)A different symbol is needed for the length
(c)AB means the segment or its length, shown by context
(d)AB can only mean the segment, never a length
4.Quadrilateral ABCD has vertices A(1, 1), B(5, 1), C(5, 4) and D(1, 4). The quadrilateral is translated by the vector $(3 - 2)$ . Which of these points is NOT a vertex of the image?
(a)(−1, 1)
(b)(3, 4)
(c)(−1, 4)
(d)(3, 7)
5.A tangent touches a circle with centre O at the point P. Q is a point on the tangent. Write down the circle fact that tells you the size of angle OPQ.
(a)A tangent always passes through the centre of the circle
(b)A tangent is always parallel to the radius it touches
(c)The angle in a semicircle is 90°
(d)The angle between a tangent and a radius is 90°
6.A scale drawing shows a room that is 5 cm wide. The real room is 15 m wide. Write the scale of the drawing in the form 1 : n.
(a)1 : 3000
(b)1 : 30
(c)1 : 300
(d)1 : 3
7.A game designer places a coin at (5, 3) on a grid. The game rotates the coin 90° clockwise about the point (2, 3) each time the player presses a button, and this is applied twice in a row. Work out the coordinates of the coin after the button is pressed twice.
(a)(1, 1)
(b)(−5, −3)
(c)(2, 0)
(d)(−1, 3)
8.Point P has coordinates (4, 2). P is rotated 90° clockwise about the point (1, 1), and the image is then reflected in the line x = 1. Work out the coordinates of the final image of P.
(a)(−2, 2)
(b)(2, −2)
(c)(2, 4)
(d)(0, −2)
9.A tangent to a circle touches the circle at exactly one point, P. Work out the size of the angle between the tangent and the radius drawn to P.
(a)180°
(b)60°
(c)90°
(d)45°
10.A water tank is a cube with edges of length 2 m. Work out how many cubic centimetres the tank holds when it is full.
(a)8,000,000 cm³
(b)8,000 cm³
(c)8 cm³
(d)80,000 cm³
11.Point A has coordinates (2, 5). Point A is translated to point B using the column vector with top number 6 and bottom number −3. Write down the coordinates of point B.
(a)(8, 2)
(b)(−1, 11)
(c)(−4, 8)
(d)(8, 8)
12.Triangle ABC has AB = 9 cm, BC = 6 cm and angle A = 35°. Triangle DEF has DE = 9 cm, EF = 6 cm and angle D = 35°. Which of the following correctly identifies the condition shown here?
(a)SSA - not sufficient to prove congruence
(b)ASA - two angles and the included side equal
(c)SAS - two sides and the included angle equal
(d)AAS - two angles and a non-included side equal
13.A cone is cut by a flat plane parallel to its circular base, partway up between the base and the apex. What shape is the cross-section?
(a)A smaller circle
(b)A triangle
(c)The same size circle as the base
(d)An ellipse
14.A cheese counter sells cheddar at £8.40 per kilogram. Work out the cost of a 350 g piece of cheddar.
(a)£24.00
(b)£2.94
(c)£29.40
(d)£2940.00
15.A sign-maker is told a metal bracket outline must have two pairs of adjacent sides equal in length (not opposite pairs), exactly one pair of opposite angles equal, and exactly one line of symmetry. Which quadrilateral matches this description?
(a)Kite
(b)Rhombus
(c)Trapezium
(d)Parallelogram

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